Algebra Examples

$12 (a - b)$ , $18 (a - b)$ , $20 (a - b)$

Step 1

Simplify each term.

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Apply the distributive property.

$12 a + 12 (- b), 18 (a - b), 20 (a - b)$

Multiply $- 1$ by $12$ .

$12 a - 12 b, 18 (a - b), 20 (a - b)$

Apply the distributive property.

$12 a - 12 b, 18 a + 18 (- b), 20 (a - b)$

Multiply $- 1$ by $18$ .

$12 a - 12 b, 18 a - 18 b, 20 (a - b)$

Apply the distributive property.

$12 a - 12 b, 18 a - 18 b, 20 a + 20 (- b)$

Multiply $- 1$ by $20$ .

$12 a - 12 b, 18 a - 18 b, 20 a - 20 b$

Step 2

Factor out the GCF of $2$ from $12 a - 12 b + 18 a - 18 b + 20 a - 20 b$ .

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Factor out the GCF of $2$ from each term in the polynomial.

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Factor out the GCF of $2$ from the expression $12 a$ .

$2 (6 a) - 12 b + 18 a - 18 b + 20 a - 20 b$

Factor out the GCF of $2$ from the expression $- 12 b$ .

$2 (6 a) + 2 (- 6 b) + 18 a - 18 b + 20 a - 20 b$

Factor out the GCF of $2$ from the expression $18 a$ .

$2 (6 a) + 2 (- 6 b) + 2 (9 a) - 18 b + 20 a - 20 b$

Factor out the GCF of $2$ from the expression $- 18 b$ .

$2 (6 a) + 2 (- 6 b) + 2 (9 a) + 2 (- 9 b) + 20 a - 20 b$

Factor out the GCF of $2$ from the expression $20 a$ .

$2 (6 a) + 2 (- 6 b) + 2 (9 a) + 2 (- 9 b) + 2 (10 a) - 20 b$

Factor out the GCF of $2$ from the expression $- 20 b$ .

$2 (6 a) + 2 (- 6 b) + 2 (9 a) + 2 (- 9 b) + 2 (10 a) + 2 (- 10 b)$

Since all the terms share a common factor of $2$ , it can be factored out of each term.

$2 (6 a - 6 b + 9 a - 9 b + 10 a - 10 b)$

Step 3

The greatest common factor $GCF$ is the term in front of the factored expression.

$2$